The goal of this review is to present an introduction to loop quantum gravity—a background-
independent, non-perturbative approach to the problem of unification of general relativity …

The problem of describing the quantum behavior of gravity, and thus understanding
quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this …

Quantum gravity poses the problem of merging quantum mechanics and general relativity,
the two great conceptual revolutions in the physics of the twentieth century. The loop and …

An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-
dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum …

A functional calculus on the space of (generalized) connections was recently introduced
without any reference to a background metric. It is used to continue the exploration of the …

Both real and complex connections have been used for canonical gravity: the complex
connection has SL (2, C) as the gauge group, while the real connection has SU (2) as the …

In Refs. 1 and 2, it was proposed that the quantum theory of gravity could take the form of a
very special type of discrete model on a triangulated 4-manifold, which has the property that …

In this topical review, we review the present status of the spin foam formulation of non-
perturbative (background-independent) quantum gravity. The topical review is divided into …

Abstract Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has
matured over the past fifteen years to a mathematically rigorous candidate quantum field …

This is an informal review of the formulation of canonical general relativity and of its
implications for quantum gravity; the various versions are compared, both in the continuum …